Question

Simplify:

(ii) $\left[\right(64{)}^{-2}{]}^{-3}÷{\left(\right((-8{)}^2{)}^3)}^2$

Answer 1

Step : Simplify the given expression

Given,

$\left[\right(64{)}^{-2}{]}^{-3}÷{\left(\right((-8{)}^2{)}^3)}^2$

$={\left[\frac{1}{(64{)}^2}\right]}^{-3}÷\left[\right(64{)}^3{]}^2[\because a^{-m}=\frac{1}{a^m}]$

$=\left(\right(64{)}^2{)}^3÷\left[\right(64{)}^3{]}^2[\because a^{-m}=\frac{1}{a^m}]$

$=(64{)}^{2\times 3}÷(64{)}^{3\times 2}[\because (a^m{)}^n=a^{mn}]$

$=(64{)}^6÷(64{)}^6$

$=\left(64{)}^{6-6}\right[\because a^m÷a^n=a^{m-n}]$

$=(64{)}^0=1$

Hence, $\left[\right(64{)}^{-2}{]}^{-3}÷{\left(\right((-8{)}^2{)}^3)}^2=1.$